You can get them by simply purchasing them from the Online Store. et them by completing social goals at a neighbor's SimTown. You can also plant a social point flower (5 LP) on a garden patch, after you have the simoleon sprout.
Since the Halloween 2016 update, the Social Point flower now costs 20 LPs to gain social points.
What You Can Spend Them OnEdit
Certain items in the Home Store can only be purchased with the new Social Points currency. These include former NBR items that you were once able to purchase based on how many "Neighbors" you had in the game, are also new homes available: Residence (- SP) or Ocean View Residence (250 SP), called the Scandinavian House, which requires Social Points to build. With the newest Life Dreams and Legacies update, the two and three story unfurnished houses have been added, and also require Social Points to build.
There are four types of houseboats available: The Tiny Tightpocket (20 SP), The Cavernous Cruiser (40 SP, two story), The Pint-Sized Prince (65 SP), and The Royal Wavecutter (100 SP, two story). They are located on the Mysterious Island at the docks and each dock has different requirements to open a houseboat.
You can also spend SP on purple colored clothing and certain furniture items.
Before the new Neighbors update, things that cost NBR did not deplete your NBR number since it was based on the number of Neighbours you had. However, buying things with the new Social Points system DOES deplete the number of Social Points you have, so you have to spend them wisely!
To get NBR items without Social Points, simply buy them before updating and move it to your inventory.